doc/en/ref_algorithm_3DVAR.rst

   1 ..
   2    Copyright (C) 2008-2018 EDF R&D
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   4    This file is part of SALOME ADAO module.
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  20    See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
  21
  22    Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  23
  24 .. index:: single: 3DVAR
  25 .. _section_ref_algorithm_3DVAR:
  26
  27 Calculation algorithm "*3DVAR*"
  28 -------------------------------
  29
  30 Description
  31 +++++++++++
  32
  33 This algorithm performs a state estimation by variational minimization of the
  34 classical :math:`J` function in static data assimilation:
  35
  36 .. math:: J(\mathbf{x})=(\mathbf{x}-\mathbf{x}^b)^T.\mathbf{B}^{-1}.(\mathbf{x}-\mathbf{x}^b)+(\mathbf{y}^o-H(\mathbf{x}))^T.\mathbf{R}^{-1}.(\mathbf{y}^o-H(\mathbf{x}))
  37
  38 which is usually designed as the "*3D-VAR*" function (see for example
  39 [Talagrand97]_).
  40
  41 Optional and required commands
  42 ++++++++++++++++++++++++++++++
  43
  44 The general required commands, available in the editing user interface, are the
  45 following:
  46
  47   .. include:: snippets/Background.rst
  48
  49   .. include:: snippets/BackgroundError.rst
  50
  51   .. include:: snippets/Observation.rst
  52
  53   .. include:: snippets/ObservationError.rst
  54
  55   .. include:: snippets/ObservationOperator.rst
  56
  57 The general optional commands, available in the editing user interface, are
  58 indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
  59 of the command "*AlgorithmParameters*" allows to choose the specific options,
  60 described hereafter, of the algorithm. See
  61 :ref:`section_ref_options_Algorithm_Parameters` for the good use of this
  62 command.
  63
  64 The options of the algorithm are the following:
  65
  66   Minimizer
  67     .. index:: single: Minimizer
  68
  69     This key allows to choose the optimization minimizer. The default choice is
  70     "LBFGSB", and the possible ones are "LBFGSB" (nonlinear constrained
  71     minimizer, see [Byrd95]_, [Morales11]_ and [Zhu97]_), "TNC" (nonlinear
  72     constrained minimizer), "CG" (nonlinear unconstrained minimizer), "BFGS"
  73     (nonlinear unconstrained minimizer), "NCG" (Newton CG minimizer). It is
  74     strongly recommended to stay with the default.
  75
  76     Example :
  77     ``{"Minimizer":"LBFGSB"}``
  78
  79   .. include:: snippets/BoundsWithNone.rst
  80
  81   .. include:: snippets/MaximumNumberOfSteps.rst
  82
  83   .. include:: snippets/CostDecrementTolerance.rst
  84
  85   .. include:: snippets/ProjectedGradientTolerance.rst
  86
  87   .. include:: snippets/GradientNormTolerance.rst
  88
  89   StoreSupplementaryCalculations
  90     .. index:: single: StoreSupplementaryCalculations
  91
  92     This list indicates the names of the supplementary variables that can be
  93     available at the end of the algorithm. It involves potentially costly
  94     calculations or memory consumptions. The default is a void list, none of
  95     these variables being calculated and stored by default. The possible names
  96     are in the following list: ["APosterioriCorrelations",
  97     "APosterioriCovariance", "APosterioriStandardDeviations",
  98     "APosterioriVariances", "BMA", "CostFunctionJ", "CostFunctionJb",
  99     "CostFunctionJo", "CostFunctionJAtCurrentOptimum",
 100     "CostFunctionJbAtCurrentOptimum", "CostFunctionJoAtCurrentOptimum",
 101     "CurrentOptimum", "CurrentState", "IndexOfOptimum", "Innovation",
 102     "InnovationAtCurrentState", "MahalanobisConsistency", "OMA", "OMB",
 103     "SigmaObs2", "SimulatedObservationAtBackground",
 104     "SimulatedObservationAtCurrentOptimum",
 105     "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum",
 106     "SimulationQuantiles"].
 107
 108     Example :
 109     ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
 110
 111   .. include:: snippets/Quantiles.rst
 112
 113   .. include:: snippets/SetSeed.rst
 114
 115   .. include:: snippets/NumberOfSamplesForQuantiles.rst
 116
 117   .. include:: snippets/SimulationForQuantiles.rst
 118
 119 Information and variables available at the end of the algorithm
 120 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 121
 122 At the output, after executing the algorithm, there are variables and
 123 information originating from the calculation. The description of
 124 :ref:`section_ref_output_variables` show the way to obtain them by the method
 125 named ``get`` of the variable "*ADD*" of the post-processing. The input
 126 variables, available to the user at the output in order to facilitate the
 127 writing of post-processing procedures, are described in the
 128 :ref:`subsection_r_o_v_Inventaire`.
 129
 130 The unconditional outputs of the algorithm are the following:
 131
 132   .. include:: snippets/Analysis.rst
 133
 134   .. include:: snippets/CostFunctionJ.rst
 135
 136   .. include:: snippets/CostFunctionJb.rst
 137
 138   .. include:: snippets/CostFunctionJo.rst
 139
 140 The conditional outputs of the algorithm are the following:
 141
 142   .. include:: snippets/APosterioriCorrelations.rst
 143
 144   .. include:: snippets/APosterioriCovariance.rst
 145
 146   .. include:: snippets/APosterioriStandardDeviations.rst
 147
 148   .. include:: snippets/APosterioriVariances.rst
 149
 150   .. include:: snippets/BMA.rst
 151
 152   .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 153
 154   .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 155
 156   .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 157
 158   .. include:: snippets/CurrentOptimum.rst
 159
 160   .. include:: snippets/CurrentState.rst
 161
 162   .. include:: snippets/IndexOfOptimum.rst
 163
 164   .. include:: snippets/Innovation.rst
 165
 166   .. include:: snippets/InnovationAtCurrentState.rst
 167
 168   .. include:: snippets/MahalanobisConsistency.rst
 169
 170   .. include:: snippets/OMA.rst
 171
 172   .. include:: snippets/OMB.rst
 173
 174   .. include:: snippets/SigmaObs2.rst
 175
 176   .. include:: snippets/SimulatedObservationAtBackground.rst
 177
 178   .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 179
 180   .. include:: snippets/SimulatedObservationAtCurrentState.rst
 181
 182   .. include:: snippets/SimulatedObservationAtOptimum.rst
 183
 184   .. include:: snippets/SimulationQuantiles.rst
 185
 186 See also
 187 ++++++++
 188
 189 References to other sections:
 190   - :ref:`section_ref_algorithm_Blue`
 191   - :ref:`section_ref_algorithm_ExtendedBlue`
 192   - :ref:`section_ref_algorithm_LinearityTest`
 193
 194 Bibliographical references:
 195   - [Byrd95]_
 196   - [Morales11]_
 197   - [Talagrand97]_
 198   - [Zhu97]_